MHD Carreau Fluid Flow Past a Melting Stretching Cylinder with Quadratic Thermal Radiation and Joule Heating
K. B. Vidya *
Department of Mathematics, Government Science College, Chitradurga-577501, Karnataka, India.
*Author to whom correspondence should be addressed.
Abstract
The present study investigates the steady, axisymmetric magnetohydrodynamic (MHD) flow of a Carreau fluid over a stretching cylinder with melting heat transfer, incorporating quadratic thermal radiation and Joule heating. The governing equations for continuity, momentum, and energy are formulated under the boundary-layer approximation. The Rosseland diffusion approximation, together with a quadratic temperature expansion, is employed to describe radiative heat transfer under significant temperature differences. Appropriate similarity transformations are applied to reduce the governing partial differential equations to a coupled system of nonlinear ordinary differential equations, which is solved numerically using the MATLAB bvp4c solver. The effects of the magnetic parameter, melting parameter, Weissenberg number, curvature parameter, quadratic radiation parameter, and Eckert number on the velocity and temperature profiles are systematically analyzed. The skin friction coefficient and local Nusselt number are also evaluated to characterize the momentum and heat transfer rates. The results indicate that an increase in the magnetic parameter reduces the fluid velocity owing to the enhanced Lorentz force, while the associated Joule heating elevates the fluid temperature and increases the thermal boundary-layer thickness. The melting parameter generally reduces both velocity and temperature distributions. In contrast, an increase in the quadratic radiation parameter enhances the temperature field by intensifying radiative heat transfer. The Eckert number also contributes to temperature enhancement through viscous dissipation and Joule heating effects, whereas variations in the Weissenberg number and curvature parameter influence the flow and thermal characteristics according to the non-Newtonian rheology and cylindrical geometry. The computed skin friction and Nusselt number reveal the combined effects of magnetic forces, melting, fluid elasticity, curvature, and thermal transport mechanisms on the surface shear stress and heat transfer rate. Furthermore, the numerical results are compared with previously published results for limiting cases, demonstrating good agreement and supporting the accuracy of the proposed numerical approach. The findings provide useful insights into the coupled influence of non-Newtonian fluid behavior, electromagnetic effects, melting, and nonlinear thermal radiation in cylindrical heat-transfer applications.
Keywords: Carreau fluid, stretching cylinder, magnetohydrodynamics, joule heating, quadratic thermal radiation, melting heat transfer, bvp4c, boundary layer flow